Elliptic equations play a central role in the study of steady-state phenomena across physics, engineering and geometry. Their analysis not only provides insights into the qualitative behaviour of ...

Liouville theorems have long been a cornerstone in the study of partial differential equations, offering fundamental insights into the nonexistence of non-trivial solutions under specific growth or ...

Liouville's formula for certain class of linear operator equations of order n is derived. The result is applied to solving a linear second order operator equation. A number of examples which ...

This paper describes the N-dimensional vectorial Sturm-Liouville problem with coupled boundary conditions. We first derive the asymptotic expressions of large eigenvalues for the vectorial ...